Final answer:
To solve the equation 5y² = -45, you divide both sides by 5 to get y² = -9, and then take the square root of both sides, which gives the solution y = ±3i.
Step-by-step explanation:
To solve the equation 5y² = -45 for y, we first need to isolate y² on one side of the equation. This can be done by dividing both sides of the equation by 5:
5y² / 5 = -45 / 5
y² = -9
Next, we take the square root of both sides to solve for y. When dealing with square roots, remember that we will get two solutions, one positive and one negative:
y = ±√(-9)
Since the square root of a negative number involves imaginary numbers, we will have:
y = ±√9 * ±√i
Thus:
y = ± 3i
Where i is the imaginary unit, which represents the square root of -1. Here, we have simplified the equation to find that y equals 3i or -3i.